Section 16.3, due December 4

It seems like finding these points and finding factors would take longer than the book says. I wasn't quite sure when the book said that they looked at 10000!P. Wouldn't that take a long time to do? This seems like one of those things where you just have to try it yourself to see that it works. Did the book choose convenient cases, or is it pretty fast to factor smaller numbers?

I got a little lost when the book started talking about singular curves. I understand that the equation has multiple roots, but should we try to use a singular curve to factor n or should we avoid them?

Section 16.2, due December 2

Is there any graphical interpretation that we can use to think of elliptic curves mod n? When I graphed the points in the example, I didn't seem to get anything.

It seems like it takes some work just changing our message into plaintext. Most other systems that we have looked at don't seem to have that problem. Does that add a lot of time or is it rather inconsequential?

Section 16.1, due November 30

I thought that was a very good introduction to elliptic curves. I did not realize that the form for an elliptic curve was y^2=x^3+... They only showed a couple of graphs of what elliptic curves can look like. I know that they said that it only makes sense graphically in the rationals or reals, but could you show more example graphs of elliptic curves in class so we could have an idea of the different possibilities they can look like.

The book said that elliptic curves can be thought of rational points, reals, or even mod p. Can you have elliptic curves in the complex plane? The book did not mention that. Would the form still be the same as a standard elliptic curve and would it look the same, too?

Section 19.3 and blog, due November 23

I must admit I did not understand a lot of this. I even found the explanation on the blog kind of confusing. I did understand, though, that we need to find the period and then can use universal exponent factorization method to factor n.

I think that this is very interesting. For a while, before I learned about PKC I wanted to be quantum physicist. I really do want to understand this better and I am glad we will be going over it in class tomorrow.

19.1-2, due November 20

Quantum cryptography is pretty cool. It is definitely the future of cryptography. I hope that we get to learn how factoring works with quantum computers. It will be fun to see the light filters tomorrow in class.

This section didn't seem very difficult. I am sure that the specifics of it are a lot more complicated. From what I have read about quantum mechanics, there are a lot of things happening that just goes against all common sense.

Section 14.1-2,due Nov. 18

The idea of a zero-knowledge protocol is very interesting. You need to be careful that you don't inadvertently give away some information in your "proof." I definitely do not like the loose application of "proof" in this section.

While the concept is easy to understand, the application seemed a bit more complicated. I had some trouble understanding what 14.2 was doing. I understand that we want to do this process in the fewest amount of applications as possible.

Section 12.1-2, due November 16

I thought that this whole idea was really interesting. Before I read the section I tried to think of how one would go about solving the problem of letting any t people know that secret, but I could not think of one. But the method is so simple that it almost seems obvious afterward.

Nothing in these sections seemed that difficult and the implementation seemed pretty straightforward.